I like tweepi.com for flushing out unfollowers. before switching to custom solutions I used that regularly and it was very effective and free
Tweepi is one of the best. Also you may try Socialoomph or Twellow. Note though that mass following and unfollowing could get your twitter account suspended.
You can once check TwtDominator , its a one of the best tool that I found. It has most of the features which makes your manual task easily with simple steps.
ManageTwitter.com has always worked well for me. Very easy to use, and it's a lot faster now than it used to be.
For a very basic, free unfollowing function I use "Justunfollow". For cleaning up my twitter account by discarding followers that are not interacting I use Hootsuite.
No, its not the tools its how you use them. Twitter androids are constantly searching twitter accounts for spam type behaviour. Keep your unfollowing to sensible levels given the size of your account. Likewise with scheduling tweets, don't use the same tweet repeatedly or across unconnected accounts. Its just common sense really, Twitter is just trying to maintain a quality experience for its users.
friendorfollow.com is free. You can put in multiple accounts and unfollow a whole mass of people. Hope this helps.